Regular Hendecagon Calculator

Name: Regular Hendecagon - Geometry Calculator
Author: Jürgen Kummer

Calculations at a regular hendecagon, a polygon with 11 vertices. Other names for polygons with eleven corners are undecagon and endecagon.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

d_{i} = a \cdot \frac{\sin (\frac{π \cdot i}{11})}{\sin (\frac{π}{11})}

h = \frac{a}{2 \cdot \tan (\frac{π}{2 \cdot 11})}

p = 11 \cdot a

A = \frac{11 \cdot a^{2}}{4 \cdot \tan (\frac{π}{11})}

r_{c} = \frac{a}{2 \cdot \sin (\frac{π}{11})}

r_{i} = \frac{a}{2 \cdot \tan (\frac{π}{11})}

Angle: 911⋅180° ≈ 147.27° 44 diagonals

π = 180° = 3.141592653589793...

Edge length, diagonals, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Heights, bisecting lines and median lines coincide, these intersect at the centroid, which is also circumcircle and incircle center. To this point, the regular hendecagon is rotationally symmetric at a rotation of 360/1 degrees (= 32,72 degrees) or multiples of this. Furthermore, the regular hendecagon is axially symmetric to the median lines. It is not point symmetric.

In the first century BC, Heron of Alexandria gave an approximate value of 66/7 a² for the area of the regular 11-sided figure, which was about 0.67 percent too high. The regular hendecagon cannot be constructed, so it cannot be drawn with compass and ruler. In contrast to the heptagon, for example, which cannot be constructed using Euclidean methods but can be constructed with aids, the hendecagon cannot be constructed even with aids. As with the heptagon, Albrecht Dürer also discovered an approximate construction for the hendecagon with an error of less than 0.2 percent.

Shown here is a coin of two Czech crowns from 2021. This coin has the shape of a regular hendecagon with rounded corners. Angular coins are called klippe, and eleven-sided coins appear occasionally.

There are four different hendecagrams or eleven-pointed stars. These are each formed from all diagonals over two, three, four or five sides. The more sides there are between the diagonals, the sharper the points of the corresponding star are.

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